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A245413 Number of endofunctions on [n] such that no element has a preimage of cardinality nine.

%I A245413 #9 Jul 23 2014 19:14:13
%S A245413 1,1,4,27,256,3125,46656,823543,16777216,387420480,9999999100,
%T A245413 285311610111,8916096934416,302874913851133,11111996418957812,
%U A245413 437893325100944175,18446712799609551616,827238486905202346257,39346304291930549899764,1978413388840508514186871
%N A245413 Number of endofunctions on [n] such that no element has a preimage of cardinality nine.
%H A245413 Alois P. Heinz, <a href="/A245413/b245413.txt">Table of n, a(n) for n = 0..200</a>
%F A245413 a(n) = n! * [x^n] (exp(x)-x^9/9!)^n.
%p A245413 b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
%p A245413       `if`(i<1, 0, add(`if`(j=9, 0, b(n-j, i-1)*
%p A245413        binomial(n, j)), j=0..n)))
%p A245413     end:
%p A245413 a:= n-> b(n$2):
%p A245413 seq(a(n), n=0..25);
%t A245413 Table[n!*SeriesCoefficient[(E^x-x^9/9!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)
%Y A245413 Column k=9 of A245405.
%K A245413 nonn
%O A245413 0,3
%A A245413 _Alois P. Heinz_, Jul 21 2014